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Converting Roman numerals to integers involves understanding both their additive and subtractive notation rules. Let’s break down LeetCode 13: Roman to Integer and solve it step by step.

🚀 Problem Description

Roman numerals are represented by seven symbols, each with a fixed value.

• Subtractive Rule: When a smaller numeral appears before a larger one, subtract the smaller numeral.

Given a Roman numeral string, return its integer equivalent.

💡 Examples

Example 1

Input: s = "III" Output: 3 Explanation: III = 3 (1 + 1 + 1). 

Example 2

Input: s = "LVIII" Output: 58 Explanation: L = 50, V = 5, III = 3. 

Example 3

Input: s = "MCMXCIV" Output: 1994 Explanation: M = 1000, CM = 900, XC = 90, IV = 4. 1994 = 1000 + 900 + 90 + 4. 

🏆 JavaScript Solution

To solve this problem, we use a mapping dictionary for Roman symbols and traverse the string to calculate the integer.

Implementation

var romanToInt = function(s) { const romanMap = { 'I': 1, 'V': 5, 'X': 10, 'L': 50, 'C': 100, 'D': 500, 'M': 1000 }; let total = 0; for (let i = 0; i < s.length; i++) { const current = romanMap[s[i]]; const next = romanMap[s[i + 1]]; if (next && current < next) { total -= current; } else { total += current; } } return total; }; 

🔍 How It Works

1. Map Roman Symbols: Use a dictionary to map Roman symbols to their values.
2. Traverse the String: For each character:
   • Add the value to the total if the current numeral is greater than or equal to the next.
   • Subtract the value if the current numeral is smaller than the next (subtractive rule).
3. Return the Total: After traversing the string, total holds the integer equivalent.

🔑 Complexity Analysis

• > Time Complexity: O(n), where n is the length of the string. We traverse the string once.
• > Space Complexity: O(1), as the mapping dictionary size is constant.

📋 Dry Run
Input: s = "MCMXCIV"

Output: 1994

✨ Pro Tips for Interviews

1. Clarify constraints: Confirm that the Roman numeral input will always be valid (as per problem assumptions).
2. Highlight efficiency: Emphasize O(n) time complexity and how the subtractive rule is handled efficiently.
3. Edge cases:
   • Smallest numeral ("I" → 1).
   • Mixed additive and subtractive cases ("XIV" → 14).

📚 Learn More

Check out the full explanation and code walkthrough on my Dev.to post:
👉 Trapping Rain Water - JavaScript Solution

What’s your approach to solving this problem? Let’s discuss! 🚀

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